1) Assuming that a variable is normally distributed: a) What Z-score separates the bottom quartile of a population from everyone else? b) What Z-score separates the top 18% of a population from...

1) Assuming that a variable is normally distributed:

1. 
   

   a) What Z-score separates the bottom quartile of a population from everyone else?

   
   


2. 
   

   b) What Z-score separates the top 18% of a population from everyone else?

   
   


3. 
   

   c) What Z-score separates the bottom 2.5% of a population from everyone else?

   
   


4. 
   

   d) What proportion of the sample will have z-scores between -0.20 and 1.64?

   
   


5. 
   

   e) What proportion of the sample will have z-scores between -0.48 and -0.08?

   
   

The next set of questions provides practice in making inferences about a larger population, based on information obtained from a random sample of that population.

2. 
   

   2) What is the relationship betweenstandard deviationandstandard error?

   
   


3. 
   

   3) A study of 365 randomly selected kindergarten students across the US revealed that they had seen an average of 3000 hours of television.

   
   
   
   
   1. 
      

      a) What is your best guess for the average amount of television viewing among all US

      
      

      kindergarteners? Explain your answer.

      
      
   
   
   2. 
      

      b) If the standard deviation in your sample is 300 hours, what is the 95% confidence

      
      

      interval (C.I.) of the expected mean television viewing for all kindergarteners in the US?

      
      

      Show your work.

      
      
   
   
   3. 
      

      c) What if the standard deviation was 600 hours? What is the new 95% C.I.? Show your

      
      

      work.

      
      
   
   
   4. 
      

      d) Take your responses from part b and c to answer this question: assuming nothing else

      
      

      changes, what happens to the width of the confidence interval as the sample deviation increases?

      
      
   
   
   
   


4. 
   

   4) On one gloomy weekend, with nothing else to do, McRee hosts a campus contest to see who can listen to the 80’s song by Barnes & Barnes titled “Fish Heads”the most number of times in a row without collapsing in agony. (Listen if you dare.) One hundred students from the student body are selected at random to participate. Upon reviewing the data, Dr. McRee discovers that that the mean number of song plays before a student collapsed in agony was 85 song plays, and the standard deviation was 9 song plays. Please answer the following questions about the probable resilience of the UP student body:

   
   

1. 
   

   a) What is your best guess for the average amount of times UP students could endure this song? Explain your answer.

   
   


2. 
   

   b) How many times could a randomly selected UP student listen toFish Headswithout collapsing, to fall within the middle 95% of all students? Show your work.

   
   


3. 
   

   c) How many times could a randomly selected UP student listen toFish Headswithout collapsing, to fall within the middle 99% of all students? Show your work.

   
   


4. 
   

   d) What if McRee’s sample size was 600? What is your 95% CI for the UP population? Show your work

   
   


5. 
   

   e) Take your responses from part b and d to answer this question: assuming nothing else changes, what happens to the width of the confidence interval as the sample size increases?

   
   

The next set of questions has you using our SPSS Add Health data to make estimates of the larger population of adolescents form which the Add Health sample was drawn. Make sure and run our SPSS syntax.

5. 
   

   5) Our syntax cleans the 19 variables in section 10 related to depression, reverse-codes some of those variables (so that the values of each question are similarly understood—higher numbers mean more feelings of depression), and creates a measure called DEPRESS.

   
   
   
   
   1. 
      

      a) Produce the mean, standard deviation, and standard error for this measure.

      
      
   
   
   2. 
      

      b) What is your best guess for the value of DEPRESS for any randomly selected respondent in your sample?

      
      
   
   
   3. 
      

      c) What is your best guess about how far your respondent’s score will be from what you reported in part b?

      
      
   
   
   4. 
      

      d) What is your best guess for the average amount of depressive affect we would find in the larger population from which Add Health was drawn?

      
      
   
   
   5. 
      

      e) With a 95% degree of confidence, the range of scores that the average level of depressive affect in the larger population is between ______ and ________. Show your work.

      
      
   
   
   6. 
      

      f) With a 95% degree of confidence, the range of scores that the average level of depressive affect in the larger population is between ______ and ________. Show your work.

      
      
   
   
   
   


6. 
   

   6) Reproduce the answers you offered for Q5a separately for males and females. Then, do the following:

   
   
   
   
   1. 
      

      a) Copy and paste your results for McRee to review.

      
      
   
   
   2. 
      

      b) One gender has a larger standard error than the other. Which one? Why (think about

      
      

      how standard errors are calculated)?